Rich Bifurcation Structure of Prey-Predator Model Induced by the Allee Effect in the Growth of Generalist Predator

Prey-predator models are building blocks for many food-chain and food-web models in theoretical population biology. These models can be divided into two groups depending on the nature of predators, namely, specialist predator and generalist predator. Generalist predators can survive in the absence of prey but specialist predators go to extinction. Prey-predator models with specialist predator and Allee effect in prey growth have been investigated by several researchers and various types of interesting dynamics have been reported. In this paper, we consider a prey-predator model with generalist predator subject to Allee effect in predator's growth rate. In general, a prey-predator system with saturating functional response can be destabilized due to the increase of the carrying capacity of prey which is known as paradox of enrichment. In our model with Allee effect in predator growth, we have shown that increase in carrying capacity of prey helps the populations to survive in a coexistence steady state. The considered model is capable of producing bistable dynamics for a reasonable range of parameter values. The complete dynamics of the system are quite rich and all possible local and global bifurcations are studied to understand the dynamics of the model. Analytical results are verified with numerical examples and successive bifurcations are identified with the help of bifurcation diagrams.